Question

You are in negotiations to make a 7-year loan of $35,000 to DeVille Corporation. To repay you, DeVille will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. You are confident the payments will be made, since DeVille is essentially riskless. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?

Answer 1

Answer:

The payments will be for  8,536.485 to achieve an 8% return on the investment.

Explanation:

we will calcualte the value of the loan at the beginning of year 4:

carrying value x (1+rate) - payment = year-end carrying value

((35,000 x 1.08 - 2,500) x 1.08-5,000) x1.08-7,500 =

(35300 carrying value at 1st year-end x 1.08-5,000) x1.08-7,500 =

33124 carrying value at 2nd year-end x 1.08-7,500 = 28273.92

Now, this will be paid with a 4 years annuity of equal payment at 8% discount rate

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $28,273.92

time 4 years

rate         0.08

$28273.92 \div \frac{1-(1+0.08)^{-4} }{0.08} = C$

C  $ 8,536.485